Andy Farrell's side boosted their Six Nations title hopes and ended France's run of 14 straight wins as they battled to a pulsating bonus-point win in Dublin.
The first half especially was two brilliant sides going toe-to-toe and producing an outstanding game of rugby.
The pace dropped in the second half a bit, but Ireland put the squeeze on and ran out worthy winners.
A bonkers first half saw the Irish lead 22-16 with Hugo Keenan, James Lowe crossing the whitewash for the hosts.
France's only try was a special one from Damien Penaud with fullback Ramos completing their tally with 11 points from the tee.
Ramos added a drop-goal after the break to narrow the gap but Garry Ringrose's late try secured the bonus-point and victory.
Caelan Doris showed outrageous strength before offloading superbly to Ringrose, and the in-form centre finished with style.